Application of dither control for automotive wiper squeal

Application of dither control for automotive wiper squeal B. Stallaert 1, F. Doucet 1, J. Rys 1, A. Diallo 2, S. Chaigne 2, J. Swevers 1, P. Sas 1 1 K.U.Leuven, Department of Mechanical Engineering, Celestijnenlaan 300 B, B-3001, Heverlee, Belgium 2 Renault, Direction de la Recherche, 1, avenue du Golf, F-78288 Guyancourt Cedex, France e-mail: Bert.Stallaert@mech.kuleuven.be Abstract This paper describes a feasibility study on dither control for automotive wiper squeal. Wiper squeal is a tonal noise caused by an unstable vibration due to the friction between wiper blade and windscreen. Dither control is the superposition of a high-frequency signal, in this case a high-frequency vibration, to stabilize a low-frequency unstability in a system. A finite element model of the wiper has been developed to facilitate the choice and design of an actuator system; piezo actuators are applied on the wiper to apply the dither signal. First experimental results show that wiper squeal can effectively be suppressed by dither control, as soon as the dither amplitude reaches a certain threshold value. 1 Introduction Car manufacturers spend a lot of effort in reducing unwanted noise inside cars. While engine noise is becoming less dominant thanks to optimized engine design and improved isolation, other noise sources are becoming more important. One of these sources are the wipers, which create two types of noise; reversal and running noise. Reversal is an impact noise caused when the wiper blade changes direction and flips over. Running noise is the common name for al types of noise produced by the wiper during movement. This last type of noise, and more specifically squeal, is investigated in this paper. Dither control is successfully applied to a squealing wiper, in order to suppress the noise. Dither control applied to a mechanical system is the superposition of a high-frequency vibration to stabilize a low-frequency vibration. Experimental and numerical studies have shown its effect on friction induced vibrations [3, 9]. Recently, dither control has effectively been applied to suppress disk brake squeal [2]. This type of non model-based control is especially interesting for squeal phenomena, since the mechanics of squeal are complex and have never been captured in a model that takes into account all effects [5]. When comparing wiper squeal to brake squeal, wiper squeal appears even more complex due to the non-linear properties of the rubber contact. The success of dither control on brake squeal led to the application to wiper squeal. In a first stage, the squeal phenomenon is investigated. From these measurements and earlier studies on dither control, it appeared that the contact force between wiper and windscreen plays an important role in the onset of squeal. Therefore, a finite element model is developed to predict this contact force distribution along the length of the wiper. This can be used to assess the effectiveness of the dither control and to facilitate the design of the control configuration. After applying piezo actuators on a wiper, an experimental study is performed to investigate the parameters influencing the dither control. The main goal of this study is to show the effectiveness of dither control applied on wiper squeal noise. It is shown that dither control can indeed suppress squeal noise, as long as the contact force variation exceeds a certain threshold value. Due to amplifier limitations, the dither frequency is limited to 2 khz. 263

264 PROCEEDINGS OF ISMA2006 The paper begins with an experimental study on the occurrence of squeal on the wiper, in order to understand the problem at hand (section 2). Section 3 describes the wiper finite element model, which is developed to support the optimization of the control configuration. Initial dither experiments and the most important observations are presented in section 4. Finally, the last section summarizes the most important conclusions. 2 Wiper squeal The term squeal usually refers to a high frequency (> 1000 Hz) tonal noise [4]. However, due to the multiplicity of terms used in literature, this paper refers to squeal noise as the noise produced by a wiper, disregarding the frequency content. Measurements have been performed in order to characterize the squeal noise. 2.1 Measurement set-up The measurement set-up is shown in figure 1, which is a standard compact three-door car. Both acoustic and vibration signals are measured; the exterior sound pressure, the interior sound pressure at the position of the driver s head and the acceleration of windscreen and wiper. The wiper used in the experiments is of the uniblade type, consisting of two thin beams with the wiper blade in between. The blade that was used is an uncoated rubber blade, which is more prone to squeal noise. The wiper used in the experiment, is already instrumented with dither actuators, in order to be able to make a correct comparison between control on and control off. Microphone Accelerometer Figure 1: Setup for wiper squeal measurements. In order to control the preload force on the wiper, a mechanism to adjust this force is required. The mechanism, shown in figure 2(a), adjusts the preload in the spring used to pull the wiper against the windscreen. Measuring the total force was done with a simple dynamometer, as shown in figure 2(b). The wiper arm is pulled from the windscreen and the force is measured at the instant that the contact is lost. 2.2 Squeal measurements The first measurement, shown in figure 3, is a time measurement of the exterior noise, to show the presence of squeal. The measurement clearly shows the difference between the reversal noise and squeal noise. The first is short and instantaneously and has a typical impact signature. The squeal noise on the other hand shows growing instability.

ACTIVE NOISE CONTROL 265 (a) With the screw, the preload force on the wiper can be adjusted. (b) Measuring the force by pulling the wiper arm from the windscreen with a dynamometer. The force is measured when contact between wiper arm and windscreen is lost. Figure 2: Adjusting and measuring the preload force on the wiper. Sound pressure [Pa] Reversal (top) Squeal + reversal (bottom) 0.2 0-0.2 17.2 17.4 17.6 17.8 18 18.2 18.4 18.6 18.8 19 Figure 3: Measured sound pressure outside the car, during one wiping cycle. Time-frequency analysis of the measured signals allows a more detailed analysis of the squeal noise. The resulting time-frequency map of the exterior sound pressure is shown in figure 4(a). The recurring cycles are clearly visible, separated by the reversal of the wiper at the bottom and at the top of the windscreen. Since the reversal is an impact phenomenon, its frequency content is large. The squeal however, is clearly a tonal noise at two distinct instances, with a frequency between 110 and 160 Hz. When the right conditions are met, squeal is observed during every wiping cycle at specific positions of the windscreen. This is important to assess the effectiveness of the applied control. The onset of squeal is most influenced by the preload force applied on the wiper. The observed frequency is low for squeal noise. However, as mentioned before, the term wiper squeal is used here for all self-excited wiper phenomena, whatever its frequency. As can be expected, the interior sound pressure and the acceleration show the same behavior (figures 4(b) (d)). The most obvious difference is the V-shaped noise at approximately 750 Hz and the low frequency signals at about 50 Hz. The first is identified as the sound of the wiper motor; its frequency content varies because of the varying motor speed, which on its turn is due to the varying load on the motor. The low frequency signal is probably related to a low frequency vibration of the wiper which does not influence the squeal phenomenon, but is clearly visible in the wiper acceleration measurements and less visible in the other measurements. 3 Wiper finite element model The experimental results of dither control on brake squeal showed that the contact force variation induced by dither control, should be some percentages of the nominal value [2]. Due to the stiff structure of a disc brake, this requirement can be easily met. The flexibility and damping of the wiper rubber however, may complicate

266 PROCEEDINGS OF ISMA2006 0.8 1000 900 800 Reversal top Reversal bottom 1000 900 800 Wiper motor 700 700 Frequency [Hz] 600 500 400 Frequency [Hz] 600 500 400 300 Squeal 300 200 200 100 100 13 14 15 16 17 18 19 (a) Sound pressure, outside car. 13 14 15 16 17 18 19 (b) Sound pressure, inside car. 1000 1000 900 900 800 800 700 700 Frequency [Hz] 600 500 400 Frequency [Hz] 600 500 400 300 300 200 200 100 100 13 14 15 16 17 18 19 (c) Acceleration, measured on wiper. 13 14 15 16 17 18 19 (d) Acceleration, measured on windscreen. the application of dither control on wipers. It is therefore relevant to know which contact force variation and which spatial force distribution can be expected when applying actuators on the wipers. Therefore, a finite element model is developed which predicts the contact force distribution along the wiper, with and without actuation. The model serves multiple purposes; most important is to assess the influence of a certain actuator force on the contact force. Secondly the model can be used in optimizing the control configuration and control design. Both a static as a dynamic finite element model are developed and implemented in Matlab. The static model calculates the resulting contact force distribution along the wiper blade, for a certain rubber type, preload force and actuation force. The dynamic model is used to calculate eigenmodes and -frequencies. After validation and updating, a good agreement is obtained with measurements, even when boundary conditions are varied. 3.1 Overview of the model Figure 4 shows a photo of the wiper, with two parallel thin beams and the rubber wiper in between. Several aspects, like the interaction between the two wiper beams and the rubber blade, and the windscreen dynamics, are not taken into account. This would only be possible with a 3D model. Therefore, several simplifications are made to develop the model shown in figure 5. The model consists of beam elements, with a non-linear spring (k rub ) in every node, representing the rubber. The mass of the beam is taken into account by the distributed load g. The piezo actuators, which are attached to the wiper system, induce a moment load M p at both ends of the actuator [7], while the addition of the actuator itself results in a local stiffening of the beam, represented by locally increasing the bending stiffness EI, with E the elastic modulus and I the moment of inertia. The inputs to the model are the preload force F c and the moment M p. An overview of the simplifications is given in following paragraphs.

ACTIVE NOISE CONTROL 267 Parallel metal beams Rubber wiper blade Figure 4: Close-up photo of the wiper, with two metal beams holding the wiper blade. Piezo actuator Beam g F c M M... p p k rub Windscreen Figure 5: Schematic representation of the simplified wiper model. Rigid windscreen The windscreen is modeled as a rigid surface, neglecting the windscreen dynamics and not taking into account any coupling between windscreen and wiper. Frequency response function (FRF) measurements of the wiper, from the actuator input to an acceleration signal on the wiper beams, show however that the windscreen clearly influences the wiper dynamics; the FRF s are significantly different when the wiper is positioned at different positions on the windscreen. By neglecting the windscreen dynamics, the model cannot be used for dynamic calculations with the wiper on the windscreen. This limits the model to calculations for the wiper in free-free boundary conditions. However, experimental investigations show that this information in itself already gives good indications to apply dither control. Simplified beam model The wiper is modeled as a simplified beam model, neglecting the fact that the wiper is composed out of two parallel beams with rubber in between. Coupling between the beams as well as wiper torsion is therefore not modeled. To include these effects, a complex 3D model would be needed, which would increase the computational burden while bringing relatively little to the model. The simplification has little effect on the applicability of the model for this feasibility study, since only normal dither is investigated (section 4.1). Only displacements normal to the windscreen are of interest, such that the torsional displacement, which results in a vibration of the wiper blade tangential to the windscreen, is of less importance. Non-linear wiper stiffness The wiper rubber is modeled as a parallel series of individual springs with nonlinear characteristics. The springs are attached to the nodes of the beam model. This assumption only neglects the damping introduced by the rubber blade and possible influences caused by the shape of the blade. The non-linear spring characteristic however, is greatly dependent on this shape and since this characteristic is experimentally determined, the shape influence is taken into account. Since the only real assumption introduced by this simplification is the absence of damping, only dy-

268 PROCEEDINGS OF ISMA2006 namic calculations are influenced. The dynamic part of the model however, is mostly limited to the calculation of eigenmodes and -frequencies, which are marginally influenced by the absence of damping. Uncoupling of the springs In a first phase the coupling of the springs is not included in the model to keep it as simple as possible. The uncoupled model results in a discontinuous force distribution when force is applied in a single point. In reality, the force distribution will be continuous and spread out over several points. A coupled model where the force is taken up by several adjacent springs is therefore closer to reality. Validation measurements show however, that the uncoupled model is already capable of predicting the force distribution with acceptable accuracy. Equivalent shape of the windscreen The deformation of the wiper results from the initial shape of the wiper, combined with the shape of the windscreen. For simplicity, the wiper is modeled as a straight beam. The influence of the initial wiper shape is taken into account by adding the initial shape to the windscreen shape, resulting in an equivalent windscreen shape. Pushing the straight wiper against this equivalent shaped windscreen causes the correct wiper deformation. This simplification remains valid as long as the deformations are small and the material behavior remains linear. Since both the curvature of the windscreen and wiper are small, this simplification is certainly valid. 3.2 Static wiper model - results The static model calculates the resulting wiper deformation and contact force distribution along the wiper for a given preload force. The force can be adjusted with the mechanism described in section 2.1. Due to the presence of the non-linear spring element, the stiffness matrix is dependent on the deformation. Therefore, an incremental procedure must be followed where the total force is applied in small steps. In each step, an iterative procedure calculates the resulting equilibrium. To evaluate the model, the resulting force distribution is compared with measured data, obtained on a measurement bench where the static force is measured along a line contact. Figure 6 shows the comparison between measured and simulated force distribution. The contact force is measured in unit force per meter of rubber. Before a model update (figure 6(a)), the model is not capable of predicting the measured force distribution. The model update however, shows that the initial wiper and windscreen shape have an important influence on the model results. After updating the wiper shape, the overall agreement between simulation and measurement is excellent, as shown in figure 6(b). The largest differences are observed at both ends of the wiper, where the model is most sensitive to the wiper shape. To validate the model both the preload force and the rubber material have been changed, resulting in the force distribution of figure 6(c). Since a different rubber type is used, an additional measurement of the rubber characteristic was required. Although the simulation and measured data differ locally, the overall agreement is still acceptable. This and other measurements indicate that both ends of the wiper and the center piece where the wiper is attached, are most difficult to model correctly. To assess the capabilities of the model to incorporate the actuator force, a validation measurement is shown in figure 6(d), where a constant voltage is sent to the piezo actuator. Although the model shows excellent agreement with the measured data, the importance of this result should not be overestimated. Since the influence of the actuator force on the force distribution is only a few percent, it is difficult to assess the significance of a difference between simulation and measurement.

ACTIVE NOISE CONTROL 269 0.8 0.9 30 25 Simulation Measurement 30 25 Simulation Measurement Fcontact(x) [N/m] 20 15 10 Fcontact(x) [N/m] 20 15 10 5 5 0 0 0.1 0.2 0.3 0.4 0.5 x [m] (a) Before update. 0 0 0.1 0.2 0.3 0.4 0.5 x [m] (b) After update. 30 25 Simulation Measurement 30 25 Simulation Measurement Fcontact(x) [N/m] 20 15 10 Fcontact(x) [N/m] 20 15 10 5 5 0 0 0.1 0.2 0.3 0.4 0.5 x [m] (c) Validation with other total force F c and rubber type. 0 0 0.1 0.2 0.3 0.4 0.5 x [m] (d) Validation with actuated piezo-actuator. Figure 6: Model validation: comparison between measured and simulated force distribution. 3.3 Dynamic wiper model - results The dynamic model calculates the FRF between the actuator force and the acceleration of a point on the wiper. Since the main goal is to identify the wiper resonance frequencies, the endpoint of the wiper is chosen in practice, where all vibration modes are visible. The model calculates both FRF s in free-free boundary conditions and in contact with the windscreen. However, due to the simplification of a rigid windscreen (see paragraph 3.1), the FRF s for the wiper in contact with the windscreen are not reliable. Figure 7 shows the comparison of a simulated and measured FRF, for a wiper with free-free boundary conditions. The model gives a good estimation of the resonance peaks, which is sufficient for the control design.

270 PROCEEDINGS OF ISMA2006 Ẍ/F Frequency Simulation Measurement Figure 7: Model validation: comparison between measured and simulated frequency response function. 4 Dither control This section gives an overview of the aspects related to dither control on wipers and presents some initial results. 4.1 Dither background Dither control is the superposition of a high-frequency signal to stabilize the low-frequency behavior of a system. Because of its simplicity, dither control is applied in different research fields [6, 8, 10]. In mechanical systems, the signal is most often a high-frequency vibration. A recent study has shown the positive effect of dither control on automotive brake squeal [2]. The dither signal, with a frequency up to 20 khz, was applied with a piezo stack integrated in the brake. The main advantage and explanation for the widespread use of dither is its simplicity: Dither is an open loop technique, requiring no extra sensors. A system or friction model is not necessary which is a major advantage for systems with friction which are often difficult to model. Since dither control is a superposition of a signal, it can often be applied on an existing structure, requiring only minor changes. Dither efficiency is determined by the dither amplitude, frequency, signal shape and the location where the dither signal is introduced in the system. Dither control comes in two considerably distinct forms, normal and tangential dither [1]. In the first case, the dither signal is applied normal to the friction surface, its effect being a modification of the friction by a reduction of the friction coefficient. In the latter case, the dither signal is applied tangential to the friction surface, its effect being a modification of the influence of friction by averaging the non-linear friction behavior. Although both directions should be considered beforehand, the application on wipers does not allow for a straightforward implementation of tangential dither, such that only normal dither is considered.

ACTIVE NOISE CONTROL 271 4.2 Dither experiments To apply the dither signal on the wipers, piezo actuators (patches) are attached to the wiper system, inducing a bending moment. This results in a high-frequency variation of the contact force between wiper and windscreen. Optimizing the actuator location is possible with the wiper finite element model; the configuration which leads to the largest contact force variation will have the highest chance of effectively suppressing the squeal noise. First dither experiments show that dither effectively suppresses squeal noise. The sound pressure measurement in figure 8 illustrates the dither effect. Before and after applying the dither signal, the squeal noise is clearly visible. Although the squeal noise disappears during the application of the dither control, it is replaced by noise generated by the dither control itself, including harmonics of the dither frequency. To avoid this dither noise, the dither frequency could lie outside the audible frequency range. However, the amplifiers used in this feasibility study did not allow driving the piezo actuators at such high frequencies. Frequency Dither signal Squeal Squeal 0 2 4 6 8 10 12 14 16 18 Figure 8: Exterior sound pressure with and without dither control. Further investigations show that the efficiency of dither control is influenced by several parameters. It was observed that a threshold value exists for the dither amplitude and that the efficiency is strongly related to the preload force and to the dither frequency. 5 Conclusions The wiper, with an uncoated blade, produces a low frequency tonal squeal noise with a frequency between 110 and 160 Hz, depending on environmental and boundary conditions. To support the optimization of the control configuration, a wiper finite element model, implemented in Matlab, is developed. It predicts the contact force distribution between wiper and windscreen, along the wiper blade, as well as the wiper resonances in free-free boundary conditions. Validation measurements show a good agreement between simulation and measurement. Finally, experimental results are presented, showing that dither is effective in suppressing wiper squeal noise. Some influencing parameters are observed, among which frequency content of the dither signal, dither signal amplitude and preload force. This paper has shown that dither control for wiper squeal is possible. However, the squeal noise is replaced by noise generated by the dither signal. Further research will focus on working around this constraint.

272 PROCEEDINGS OF ISMA2006 The developed FE model allows to predict which configuration leads to the maximum contact force variation. This information can be used to enhance the efficiency by an optimal placement of actuators. Acknowledgements The research of Bert Stallaert is funded by the Institute for the Promotion of Innovation through Science and Technology in Flanders (IWT-Vlaanderen). References [1] B. Armstrong-Hélouvry, P. Dupont, C. Canudas-de-Wit, A survey of models, analysis tools and compensation methods for the control of machines with friction, Automatica, Vol. 30, No. 7, 1994, pp. 1083-1138. [2] K. Cunefare, A. Graf, Experimental active control of automotive disc brake rotor squeal using dither, Journal of Sound and Vibration, Vol. 250, No. 4, 2002, pp. 570-590. [3] B.F. Feeny, F.C. Moon, Quenching stick-slip chaos with dither, Journal of Sound and Vibration, Vol. 237, No. 1, 2000, pp. 173-180. [4] S. Goto, H. Takahashi, T. Oya, Clarification of the mechanism of wiper blade rubber squeal noise generation, JSAE Review, Vol. 22, No. 1, 2001, pp. 57-62. [5] N.M. Kinkaid, Automotive disc brake squeal, Journal of Sound and Vibration, Vol. 267, No. 1, 2003, pp. 105-166. [6] L.A. Maccoll, Fundamental theory of servomechanisms, Van Nostrand, New Yord, 1945. [7] A. Preumont, Vibration control of active structures, 2nd edition, Kluwer Academic Publishers, 2002. [8] H. Seilmann, A. Bajsarowicz, Electromechanical tuning element (EMT) with extended range for dither stabilization of lasers, Review on Scientific Instrumentation, Vol. 55, 1984, pp. 1551-1555. [9] J.J. Thomsen, Using fast vibrations to quench friction-induced oscillations, Journal of Sound and Vibration, Vol. 228, No. 5, 1999, pp. 1079-1102. [10] P.C. Tung, S.C. Chen, Experimental and analytical studies of the sinusoidal dither signal in a DC motor system, Dynamics and Control, Vol.3, 1993, pp. 53-69.